Hamiltonian elliptic systems with critical polynomial-exponential growth. (January 2022)

• Record Type: Journal Article
• Authors: do Ó, João Marcos; Macedo, Abiel; Ribeiro, Bruno
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 35B33 -- 35J50 -- 35J62 -- 35J35; Hamiltonian elliptic systems -- Reduction by inversion -- Fourth-order nonlinear PDE -- Variational methods -- Exponential growth -- Regularity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112579
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work, we revisit a classical problem of Hamiltonian-type systems of second-order elliptic PDE in bounded domains. Recalling the famous critical hyperbola associated with this problem, we propose an approach where one of the nonlinearities has a polynomial growth over this hyperbola's asymptotes, which allows the other one to have exponential growth. We establish solutions for these critical systems by using the reduction by inversion method and some new results for sharp Adams Inequality and Concentration–Compactness for high order N -Laplace operators.